If $f: R \rightarrow R$ is given by $f(x) = (3 - x^{3})^{\frac{1}{3}}$,then $fof(x)$ is ..........

If $f(x) = \frac{1+x}{1-x}$ where $x \neq 1$,then $f(x) \cdot f(y) = $ . . . . . . .

Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f, g : N \to N$ such that $f(n) = \begin{cases} \frac{n+1}{2} & \text{if } n \text{ is odd} \\ \frac{n}{2} & \text{if } n \text{ is even} \end{cases}$ and $g(n) = n - (-1)^n$. Then $fog$ is

If $g(x)=x^2+x-1$ and $(g \circ f)(x)=4 x^2-10 x+5$,then $f(2)$ is equal to

Let $D = \mathbb{R} - \{0, 1\}$ and $f: D \rightarrow D$,$g: D \rightarrow D$,and $h: D \rightarrow D$ be three functions defined by $f(x) = \frac{1}{x}$,$g(x) = 1 - x$,and $h(x) = \frac{1}{1 - x}$. If $j: D \rightarrow D$ is such that $(g \circ j \circ f)(x) = f(x)$ for all $x \in D$,then which one of the following is $j(x)$?

$f(x) = (20 - x^4)^{1/4}$ for $0 < x < \sqrt{5}$,then $f(f(1/2))$ is equal to